Vibrating ring gyroscopes are known in which a ring is vibrated in a primary flexural mode by a primary drive means. Rotation of the gyroscope about the ring axis results in Coriolis coupling of the primary flexural mode into a secondary flexural mode. The vibrations in the secondary mode are detected by a secondary pickoff means and are related to the rotation of the gyroscope. Arrangements are known in which closed loop control is used to both maintain a specific amplitude of the primary mode, and to null the secondary mode.
A cos 2θ in-plane flexural mode is typically used in vibratory ring gyroscopes, with a secondary mode at a 45° angular offset to the primary mode. A geometrically perfect ring consisting of a perfectly isotropic material will have primary and secondary cos 2θ modes that are perfectly matched in frequency and the cos 2θ mode can therefore be excited at any arbitrary orientation. However, in reality, ring structures are not geometrically perfect, and their materials may not be isotropic.
A gyroscope may for example be formed in silicon at a slight angular offset to the [111] crystal plane (in which plane silicon is isotropic), thereby resulting in a cos 4θ variation in Young's Modulus around the ring. An etching process used to form such a silicon gyroscope may be subject to variation across a device, leading to variable trench width, sidewall profile or notching, Differential thermal expansion between the ring structure and the other components to which it is attached may give rise to anisotropic stresses applied to the ring structure. These imperfections give rise to variations in the distribution of mass and/or stiffness throughout the ring. These imperfections will give rise to a normal in-plane cos 2θ mode which is fixed at a specific angle, and a further normal in-plane cos 2θ mode at a 45° angle to the normal mode and which has a higher natural frequency.
The defects described hereinbefore are difficult to control, and it is therefore hard to ensure that the normal cos 2θ modes of the ring coincide with the alignment of the primary and secondary drive and pickoff means. Although the vibrations resulting from excitation of the ring by the primary drive are the superposed response of both of the natural modes of the ring, the resulting vibration tends to be a close approximation of one of the normal modes.
References to the primary and secondary response modes hereinafter refer to the vibrations arising from excitation of the ring by the primary or secondary drive means respectively.
This misalignment between the primary and secondary drive means and the primary and secondary response modes gives rise to quadrature bias error, which may in turn give rise to rate bias errors. Such bias errors are a key performance constraint in gyroscope performance. Although the bias errors vary with temperature, the dominant factor determining bias error is the initial frequency matching and alignment of the normal modes. Furthermore, Coriolis coupling between the primary and secondary modes is improved when the frequency split therebetween is small. A method of tuning vibratory ring structures to match the primary and secondary mode frequencies and to align the normal modes with the primary and secondary drive and sense means is therefore desirable.
A number of methods for tuning vibratory ring structures have been suggested. In EP1775551 a vibratory ring gyroscope is disclosed in which capacitive transducers are used to tune the modes of the ring. U.S. Pat. No. 5,739,410 and GB2460935 disclose methods of tuning a vibratory ring structure by removing or adding material to the neutral axis of the ring, thereby modifying only the effective mass. Similarly, “Multimodal Tuning of a Vibrating Ring using Laser Ablation”; Proceeding of the Institution of Mechanical Engineers Part C, Journal of Mechanical Engineering Science 2003 Jan. 1, Gallacher at al, describes a laser ablation technique for use in tuning of a vibratory ring structure.
A practical method of tuning a vibratory ring structure that is both straightforward to implement, and which enables a high degree of accuracy in matching the primary and secondary mode frequencies is desirable.